"Set versions of star compact and star Lindelöf properties"Maesano, FortunatoGiven a topological space $X$ and an open cover $\mathcal{U}$ of it, the star of a subset $A$ of $X$ with respect to $\mathcal{U}$ is the set $st(A, \mathcal{U}) = \bigcup \{ U \in \mathcal{U} : U \cap A \neq \emptyset \}$. For a space, the properties to be covered by stars founded on a finite or a countable subset of the cover are called star compact and star Lindelöf properties, both are weaker tha countable compactness and stronger than their pseudo covering property counterpart (see [vDRRT]). We present a new class of star covering properties, namely the set star covering properties, wich were introduced by Kocinac, Konca and Singh, and consist on a generalization both of the previously cited ones and other already known. This is a joint work with M. Bonanzinga (University of Messina). |
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